WASHINGTON — It was a bipartisan spectacle, one served up for Americans craving cooperation in an era of divided government and persistent gridlock.

From one end of Pennsylvania Avenue to the other, President Barack Obama and Republicans in Congress made what seemed like an attempt to work together. Republicans dined at and a few blocks from the White House and the president visited Capitol Hill, each side essentially on the other's home turf. Talk – in public at least – focused on areas of possible collaboration. The phrase "grand bargain" was tossed around as if big, across-the-aisle deals were in the works.

If only it actually had meant a sea change. But in reality, the past few weeks simply shone the spotlight on the tension of this nation's say-one-thing-do-the-other politics.

Both Obama and House Speaker John Boehner tempered expectations – and put the onus on others to find common ground.

"We've had good conversations. But ultimately it's a matter of the House and Senate, both caucuses, getting together and being willing to compromise," Obama said, a measured prod as he left Capitol Hill after three days of meetings last week that, like the bipartisan meals of the week before, he had initiated.

Boehner was blunt: "This is going to take more than dinner dates and phone calls. It's going to take the president and Senate Democrats rolling up their sleeves, making tough choices about how we solve our nation's problems."

At the same time, Republicans and Democrats did the very opposite of reach for the middle. Each side offered up competing budget proposals filled with ideas drawn narrowly from their ideological wings. Both sides dug in on their positions.

Obama also spent time bucking up his biggest backers, who had huddled to plot how to help his agenda through Congress. Fighting for the middle class was the phrase of choice – as they gathered for two days in the posh St. Regis hotel. Organizers sought to appear nonpartisan, promising to work with people of all political stripes, albeit those who wanted to help enact "a progressive agenda." That's essentially code for Democrats who back Obama's proposals.

"What we want is to make sure that the voices of the people who put me here continue to be heard," Obama told the gathering.

Meanwhile, the Republican Party's leaders of yesterday and tomorrow courted conservative activists during an annual conference that was both a pep rally for the GOP's most ardent backers and a three-day skewering of Democrats even as questions about the party's direction hung heavy. So-called red meat – sound bites, refrains and slogans served up to energize supporters and demonize opponents – topped the menu.

"Don't tell me Republicans are out of ideas when the entire Democrat agenda was articulated during the Truman administration," the top Senate Republican, Mitch McConnell, said. "Don't tell me Democrats are the party of the future, when their presidential ticket for 2016 is shaping up to look like a rerun of the `Golden Girls.' We've got Rand Paul, Marco Rubio, Paul Ryan and a slew of smart, young and energetic governors ready to take America into the future. They've got Hillary and Joe Biden."

The lesson: The pressures of a system dominated by the far wings of their political parties – where liberals hold the power among Democrats and conservatives hold the power among Republicans – cause leaders to speak out of both sides of their mouths. This has become the case all too often, even though the general public says it wants collaboration and some politicians truly want to collaborate.

So is the system itself preventing it?

For both sides, the mirage of bipartisanship is a political necessity. Polls show that Americans are deeply sour on the Republican Party. Now people are turning on Obama, too; he has lost his postelection bump in surveys. So, with their actions of comity, they're both trying to send a message: We get that you want us to work together.

But, as is usually the case in politics, the show obscures the truth.

Both sides feel intense pressure to rile up their core supporters, perhaps even more than the pressure they feel to address the nation's problems. Here's why: Those who are the most polarized in America are also the most passionate, motivated to raise money, knock on doors and spread the message of their favored candidates. That means those are the people who wield the most influence over politicians – the ideological and the involved.

Not so much for the rest of the country. Centrist America is not at all homogenous in its views. It's certainly not passionate about the middle of the road. And because of that, it's much less willing to spend its time working for it. Nobody in this group marches en masse to chant, fervently, "We want common ground" – which by definition means all sides bending a bit in their beliefs.

This is not a new phenomenon.

In May 1968, Richard Nixon spoke of a "silent center" – "the millions of people in the middle of the American political spectrum who do not demonstrate, who do not picket or protest loudly."

With polarization and disgust with Washington at a high level – common wisdom in recent years has suggested that the public's appetite was ripe for supporting politicians focused on the middle ground. Yet even when conditions are ripe for compromise, and people are willing to compromise, our nation struggles with it.

Even when the center of the electorate does get a burst of passion, often there's nothing for it to stick to because – in this system, at least – no candidate who takes the middle ground makes it very far. Efforts to draft like-minded candidates, through groups called Unity08 and Americans Elect, fizzled. And No Labels – described as Democrats, Republicans and "everything in between dedicated to the politics of problem-solving" – has generated little, if any, traction.

Three times in as many months, Congress passed laws with bipartisan support: expanding the Violence Against Women Act, extending Superstorm Sandy aid and avoiding a "fiscal cliff" of automatic tax increases and spending cuts that economists said would have set back the slow-growing economy. Democrats drove the train on all three; Boehner, recognizing the perilous politics for his party should he block votes, agreed to break his usual stance that he wouldn't bring a measure to the floor without most Republicans supporting it.

What's more, Republicans and Democrats also are showing signs of coming together to overhaul the immigration system, if not other matters like cybersecurity.

Such developments may suggest the starting point of a period of increased compromise – the conflicting images of the past few weeks, and Washington's history of speaking out of both sides of its mouth, aside. Silent though it may be, the center still pulls.

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EDITOR'S NOTE – Liz Sidoti is the national politics editor for The Associated Press. Follow her on Twitter: http://twitter.com/lsidoti